Key Concepts in Mathematics

Arithmetic: Basic operations (addition, subtraction, multiplication, division).
Algebra: Study of symbols and rules for manipulating those symbols; involves solving equations.
Geometry: Study of shapes, sizes, and properties of space; includes points, lines, angles, and surfaces.
Trigonometry: Study of relationships between angles and sides in triangles; involves functions such as sine, cosine, and tangent.
Calculus: Study of change and motion; includes differentiation and integration.
Statistics: Study of data collection, analysis, interpretation, presentation, and organization.
Probability: Study of uncertainty and the likelihood of events occurring.

Order of Operations: PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Number Types:
- Natural Numbers: Counting numbers (1, 2, 3,...).
- Whole Numbers: Natural numbers plus zero (0, 1, 2, 3,...).
- Integers: Whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3,...).
- Rational Numbers: Numbers that can be expressed as a fraction (e.g., 1/2, 0.75).
- Irrational Numbers: Numbers that cannot be expressed as a simple fraction (e.g., √2, π).

Equations: Mathematical statements that assert the equality of two expressions.
Functions: Relations that assign every input exactly one output; denoted as f(x).
Polynomials: Expressions consisting of variables raised to whole number exponents; e.g., ax^n + bx^(n-1) + ... + c.

Shapes:
- 2D: Circles, squares, triangles, rectangles.
- 3D: Spheres, cubes, cylinders, cones.
Theorems:
- Pythagorean theorem (a² + b² = c² in right triangles).
- Area and perimeter calculations for various shapes.

Limits: The value that a function approaches as the input approaches some value.
Derivatives: Measure of how a function changes as its input changes.
Integrals: Represents the area under a curve; used for accumulation of quantities.

Descriptive Statistics: Summarizes data using measures like mean, median, mode, and standard deviation.
Inferential Statistics: Makes predictions or inferences about a population based on a sample.

Basic Concepts:
- Experiment: A procedure that produces outcomes.
- Event: A specific outcome or a set of outcomes.
Probability Formulas:
- P(A) = Number of favorable outcomes / Total number of outcomes.

Graphs: Visual representations of data or functions; includes line graphs, bar graphs, and scatter plots.
Calculators and Software: Tools that assist in performing complex calculations and visualizations.

Arithmetic: Involves basic operations such as addition, subtraction, multiplication, and division.
Algebra: Focuses on symbols and the rules for manipulating them; primarily centers around solving equations.
Geometry: Examines shapes, sizes, and the properties of space, including points, lines, angles, and surfaces.
Trigonometry: Investigates the relationships between angles and sides in triangles using functions like sine, cosine, and tangent.
Calculus: Concerns the study of change and motion through differentiation and integration.
Statistics: Encompasses data collection, analysis, interpretation, presentation, and organization.
Probability: Explores uncertainty and the chances of event occurrences.

Order of Operations: Remember the sequence PEMDAS—Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.
Number Types:
- Natural Numbers: Counting numbers starting from 1.
- Whole Numbers: Natural numbers including zero.
- Integers: Whole numbers with their negative equivalents.
- Rational Numbers: Numbers expressible as a fraction.
- Irrational Numbers: Non-fractionable numbers, such as √2 and π.

Equations: Assertions of equality between two mathematical expressions.
Functions: Relationships assigning exactly one output for each input, represented as f(x).
Polynomials: Algebraic expressions with variables raised to whole number exponents.

Shapes:
- 2D Shapes: Examples include circles, squares, triangles, and rectangles.
- 3D Shapes: Include spheres, cubes, cylinders, and cones.
Theorems:
- Pythagorean Theorem: In right triangles, a² + b² = c².
- Calculations for area and perimeter are essential for various shapes.

Limits: Values a function approaches as its input nears a certain value.
Derivatives: Reflect how a function changes in response to changes in its input.
Integrals: Calculate the area under a curve, crucial for understanding accumulation.

Descriptive Statistics: Summarizes data with measures like mean, median, mode, and standard deviation.
Inferential Statistics: Utilizes sample data to make predictions or inferences about a larger population.

Basic Concepts:
- Experiment: Any procedure yielding outcomes.
- Event: A specific outcome or set of outcomes.
Probability Formulas: The probability of an event A is given by P(A) = Number of favorable outcomes / Total number of outcomes.

Graphs: Visual data representations, including line graphs, bar graphs, and scatter plots.
Calculators and Software: Assist with complex calculations and data visualizations.

π (Pi): Approximately 3.14159, representing the ratio of a circle's circumference to its diameter.
e (Euler's Number): Approximately 2.71828, serving as the base of natural logarithms.